1. Field of Invention
The present invention relates to a method and an apparatus for digital signal processing and more particularly to a method and an apparatus for utilizing low-resolution digital signals to get the same output result as high-resolution digital signals.
2. Description of Related Art
Sound and light both are waves. There are two ways to store these analog signals; one way is analog storage, and the other way is digital storage. For example, a conventional analog storage medium for audio signals uses magnetic characteristics of a storage media to record directly the audio signals. These storage media, such as disks, tapes, and videotapes, are easily distributed, but the frequencies recorded by them are limited and are easily distorted by damage. These storage media thus can be used for only a short time. A digital storage medium uses digital signals composed of binary digits 0 and 1 to record the audio signals, examples thereof being compact discs, digital compact cassettes, digital audio tapes, and hard disks. The audio signals stored by these digital storage media are preserved well and the reproduction quality thereof is also better.
The audio signals stored by the digital storage are stored as digital signals, but audio signals in nature are transferred in analog signal form. If the audio signals are stored in digital signal form, the first step in the process is to convert the analog audio signals to the digital signals. The conversion is called an analog-to-digital conversion. The analog-to-digital conversion first samples the analog signals. Taking audio signals as an example, the sampling of the audio signals has two main factors: sampling rate and sampling resolution.
Sampling is how analog information is digitized. Digitization is performed by sampling at discrete intervals. To digitize sound, for example, a device measures amplitudes of sound waveforms many times per second. These numeric values can then be recorded digitally. The sampling rate is therefore defined as a frequency of sampling the waveform of the audio signals per second. When the sampling rate of the audio signal is higher, the sound quality output by the recorded digital signals is clearer, but the data size thereof is larger. In addition, the sound quality output by the digital signals only can achieve a result of a half of the actual sampling rate, and a double sampling rate is therefore used to reproduce original sound precisely. For example, the hearing limitation of humans is about 20 KHz, so the sampling rate for the preferred sound quality should be more than 40 KHz.
The sampling resolution determines whether the sampled audio signals preserve the original waveforms well. If the sampling resolution is higher, the waveforms reproduced from the sampled digital signals are closer to those of the original audio signals. If the sampling is carried out at the 8-bit rate, a quantity of combinations it can represent is 28, i.e. 256. That means an 8-bit resolution is only able to differentiate 256 levels of sound. If the sampling is carried out at a 16-bit rate, a quantity of combinations it can represent is 216, i.e. 65536, and the accuracy of the sampling is naturally improved.
According the foregoing two main factors of the sampling of the audio signals, sampling rate and sampling resolution, common digital audio signals, such as CD-quality audio signals, radio-quality audio signals, and telephone audio signals, are listed in Table. 1 to compare differences therebetween.
TABLE 1Common digital audio signals.SamplingSamplingAmount of DataSound TypeRateResolutionChannelsper SecondCD-quality44,10016 bitsStereo44,100*16*2 =1,411,200 bitsRadio-quality22,0508 bitsMono22,050*8*1 =176,400 bitsTelephone-quality11,0258 bitsMono11,025*8*1 =88,200 bits
Form the Table. 1, the specification, such as sampling rate, sampling resolution and channels, of the CD-quality audio signals is superior to those of the radio-quality audio signals and the telephone-quality audio signals. The sound quality of the audio signals stored in CD-quality is clearer and more precise, but the amount of data per second thereof is further larger than for the others, and a larger storage space is therefore needed to store the CD-quality audio signals.
When the foregoing digital audio signals are output, for example, the foregoing audio signal stored in the compact discs or the hard disks are output by a speaker, the digital audio signals need to be converted back to the original analog audio signal for outputting, and the conversion step is called a digital-to-analog conversion (DAC).
When the digital-to-analog conversion is performed, if the sampling resolution thereof is higher, i.e. there are more sampling bits, the cost of the conversion circuit is higher as well. For example, the amount of circuit mirrors utilized in an 8-bit conversion circuit is only a quarter of the amount of circuit mirrors utilized in a 10-bit conversion circuit, and every circuit mirror occupies a particular unit area. In other words, the layout of the 10-bit conversion circuit is larger than the layout of the 8-bit conversion circuit by 768 unit areas, so the manufacturing cost of the 10-bit conversion circuit is substantially raised. For a manufacturer, the high-resolution digital-to-analog conversion, conversion with more bits, is thus a big burden on manufacturing cost thereof.